Answer: There are a number of plants you could use in a shady area that would help cover the soil such as Hedera helix, Vinca minor, Hostas, Ferns, or Lysimachia nummularia "Aurea". While you are waiting for the plants to become established and form a covering layer, you should mulch in between them with an organic mulch. YOu will also need to loosen the soil and work in ample organic matter such as compost prior to planting.
Before planting you might also want to see if the drainage patterns up hill from there can be adjusted to avoid causing such rapid erosion-causing runoff along that area. If the water moves too quickly at high volume, it may wash away your plants.
Also, if it is bare along the fence and only along the fence, you might want to investigate if someone used a long term weed killer in that area at one time. I mention this because it is sometimes done along fences and could prevent your new plants from growing.
Your local professionally trained nursery staff should also be able to make suggestions based on a more detailed understanding of the growing conditions and your overall design goal. Good luck with your project!
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